Respuesta :
The complete question is
"Which values of x and y would make the following expression represent a real number? (4 + 5i)(x + yi)"
The value of x and y are all points that satisfy the equation would be,(4,-5).
How to find the simplify the expression?
Use the distributive property to simplify the expression.
The given expression is,
(4 + 5i)(x + yi)
4(x + yi)+ 5i (x + yi)
4x + 4yi + 5xi + 5yi^2
We know that i^2 = -1
4x + 4yi + 5xi - 5y
(4x - 5y) +i ( 4y + 5x)
In x+iy, x is the real part and y is the imaginary part.
If the given expression represents a real number it means the imaginary part must be zero.
4y + 5x= 0
All the points which satisfy the above equation are the values of x and y for which the given expression is a real number.
For eg. (4,-5)
4y + 5x
4(-5) + 5(4)
= 0
LHS=RHS, which means the point satisfies the equation and the value of x and y are (4,-5).
Learn more about expression ;
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Answer:
x = 4, y = -5 or the 3rd option
Step-by-step explanation:
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